Modelling the injection of a tracer in a well: a new mathematical and numerical approach.

A new mathematical approach is proposed to model the injection of a tracer in a well for field tracer tests. It is based on the water and tracer mass budget integrated over the injection well, for the different injection steps (tracer injection, water flush and tracer behaviour after the injection). This physical approach deals with well-bore mixing and dilution effects, local distortion of the flow field around the injection well, back-diffusion of the tracer in the injection well after the injection, and tracer capture in the well bore. A numerical solution (finite differences over time) is proposed and implemented in a three-dimensional finite element flow and transport simulator (SUFT3D). A radially converging tracer test is computed to illustrate the adequacy and usefulness of this new mathematical concept to model field results.